From a group of 88 men and 77 women, 5 persons are to be selected to form a committee so that at least 44 men are there on the committee. In how many ways can it be done?
Answer:
546546
- We are required to select a 55-member committe from a group of 88 men and 77 women with at least 44 men. This can be done in 22 different ways:-
- 44 men and 11 woman
- 55 men
- Number of ways of selecting 44 men and 11 woman =8C4×7C1=8C4×7C1 =8!4!(8−4)!×7!1!(7−1)!=490=8!4!(8−4)!×7!1!(7−1)!=490
Number of ways of selecting 55 men =8C5=8C5 =8!5!(8−5)!=56=8!5!(8−5)!=56 - Now, required number of ways of selecting a 55-member committee =490+56=546=490+56=546
Hence, there are 546546 ways of selecting a 55-member committee with at least 44 men.